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Vorticity Advection

leads to rising/falling pressures at the surface

Vorticity is the localized rotation of the air. Air that
rotates counterclockwise, such as in
cyclones and troughs, is said to
have positive vorticity. Clockwise rotating air, such as in
high pressure
systems and ridges, has negative vorticity.
The advection of vorticity
at high levels will result in a response at the surface which will
attempt to offset the effects of the advection.
More specifically, vorticity advection is indicative of
rising motion/falling pressures at the surface. For example, look at
this 500 mb map for 12Z, October 29, 1995.